We bought our TT when my youngest (of 3) was 1 yr old and towed with a crew cab pickup. When that pickup was ready to be replaced, we only considered 3-row SUVs. My wife insisted that since the bulk of our car travel time was towing, 3 rows was a lot more pleasant. She won and 4 years later we are still kind of sane. 3rd kid did change the dynamics of our family a lot. Logistically, our US society caters to a family unit of 4 from hotel rooms to dining restaurants.
I looked at rear king slide TTs like the Outback 250, but the privacy and access on the road turned me off. Now that we have the more capable 3/4 ton Suburban for something like your original Bullet 34, we have really made the current floorplan work well for us. Pack and play fits on the floor or jackknife sofa or dinette. We have slept 8 in a pinch. Your payload should be in the 1400 pound range, and my TT should tow well behind your Suburban. Stay in the 5000-5500 pound dry range.